Study MaterialsCBSE NotesProbability Class 10 Notes Maths Chapter 15

Probability Class 10 Notes Maths Chapter 15

 

CBSE Class 10 Maths Notes Chapter 15 Probability

Probability: It is the numerical measurement of the degree of certainty.

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    • Theoretical probability associated with an event E is defined as “If there are ‘n’ elementary events associated with a random experiment and m of these are favourable to the event E then the probability of occurrence of an event is defined by P(E) as the ratio \(\frac { m }{ n }\) “.
      Probability Class 10 Notes Maths Chapter 15 1
    • If P(E) = 1, then it is called a ‘Certain Event’.
    • If P(E) = 0, then it is called an ‘Impossible Event’.
    • The probability of an event E is a number P(E) such that: 0 ≤ P(E) ≤ 1
    • An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
    • For any event E, P(E) + P(\(\bar { E }\)) = 1, where \(\bar { E }\) stands for ‘not E’. E and \(\bar { E }\) are called complementary events.
    • Favourable outcomes are those outcomes in the sample space that are favourable to the occurrence of an event.

    Sample Space
    A collection of all possible outcomes of an experiment is known as sample space. It is denoted by ‘S’ and represented in curly brackets.
    Examples of Sample Spaces:
    A coin is tossed = Event
    E1 = Getting a head (H) on upper face
    E2 = Getting a tail (T) on upper face
    S = {H, T}
    Total number of outcomes = 2

    Two coins are tossed = Event = E
    E1 = Getting a head on coin 1 and a tail on coin 2 = (H, T)
    E2 = Getting a head on both coin 1 and coin 2 = (H, H)
    E3 = Getting a tail on coin 1 and a head on coin 2 = (T, H)
    E4 = Getting a tail on both, coin 1 and coin 2 = (T, T)
    S = {(H, T), (H, H), (T, H), (T, T)}.
    Total number of outcomes = 4

    NOTE: In probability the order in which events occur is important
    E1 & E3 are treated as different outcomes.

    Important Tips

    • Coin: A coin has two faces termed as Head and Tail.
    • Dice: A dice is a small cube which has between one to six spots or numbers on its sides, which is used in games.
    • Cards: A pack of playing cards consists of four suits called Hearts, Spades, Diamonds and Clubs. Each suite consists of 13 cards.

     

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